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设三角矩阵 {x_k~((n)},k=1,2,…,n,n=2,2,…的第n行为n次多项式T_n(x)=cos(n arc cos x)的根 相似文献
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1 引 言在 1 982年 ,Hakopian[1 ]提出了一种新的多元插值 这种插值是Kergin插值的一种发展 ( [2 - 4 ]) 王和来 [5]在 1 984年给出了这种插值的余项估计 梁在 [6 ]的基础上于 86年给出了二元Hakopian插值的Lagrange型表达式并对定义于单位圆盘上足够光滑的插值函数给出了它的收敛速度估计 [7] 圆盘上的二元Hakopian插值的导数收敛性在 [8]中进行了讨论 最近 ,在 97年 ,梁和吕 [9]进一步研究了Hakopian插值的积分收敛性 我们在这篇文章中对Hakopian插值的弱收敛性进行了研… 相似文献
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The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm. 相似文献
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Ying-guang Shi 《计算数学(英文版)》2001,19(2):151-156
1. IntroductionThis note deals with convergence of (0,1,2,3) illterpolation on an arbitrary system of nodes.Fisrt we illtroduce some definitions and notations.LetGiven a fiXed even integer m, let Ajk 6 Pm.--1 (the set of polynomials of degree at most mn-- 1)satisfyThen the (0,1,...,m--1) Hermite--Fej6r type illterpolation for f 6 C[--1, 1] is defined byand the (0,1,...,m--1) Hernilte interpolation for f e Cd--'[--1, 1] is defined by(of. [6]). We also need a well known fact:where 11' 11 sta… 相似文献
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Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein when n →∞ and convergence rate of Bn(f,q;x) when f ∈ Cn-1[0, 1], q →∞ are also presented. 相似文献
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设给定函数F(t),它在[0,1]上有各阶导数,作级数: sum from j=0 to ∞[F~(2j)(0)f_(2j 1)(t) F~(2j)(1)g_(2j 1)(t)],0≤t≤1, (1)其中f_(2j 1)(t)与g_(2j 1)(t)为[1]中定义的2n 1次多项式。[2]中给出了下述定理: 定理A.已给函数F(t),0≤t≤1。若偶阶导数序列{F~(2j)(t)}在[0,1]上一致有界,即存在M>0,使得 相似文献
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Yongping Feng+ 《计算数学(英文版)》2003,21(2):145-156
In this paper the uniform convergence of Hermite-Fejer interpolation and Griinwald type theorem of higher order on an arbitrary system of nodes are presented. 相似文献
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Lagrange插值逼近导数的平均收敛 总被引:1,自引:0,他引:1
<正>We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived. 相似文献
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In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented. 相似文献
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关于代数体函数的微分多项式 总被引:1,自引:0,他引:1
本文证明υ值代数函数的微分多项式是一λ值(1≤λ≤υ)代数体函数,即υ值代数体函数ω=ω(z)的微分多项式p(ω)可以被如下方程确定:[ελ(z)p^λ ελ-1(z)p^λ-1 … ε0(z)]^k=0这里ε0(z),ε1(z),…,ελ(z)为整函数且无公共零点,λ和k为正整数且λk=υ。 相似文献
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一种二次保形插值参数曲面 总被引:1,自引:0,他引:1
1.引言保形插值是工业设计和制造中经常遇到的问题,有关这方面的研究已有许多文献【‘-u1.设n二Fx;,yi,人,川7一0,1,…;n;j=0;l,…,。;x;<x;+1.l=0,1,….n—1;yi<的十;,J二O,L…,。一卫}是一给定的数据集,Cadson和[ltsch、Beatson和zejerJ-1985年分别提出的方法只保持被插数据集的轴向单调性;Dodd和Roulier等人于1983和1987年提出的方法只保持被插点集网格线上的轴向凸凹性和单调性;Constantini和FOntanella于1990年提出的方法可保持被插点集在所有于区域的边界及共内部的轴向凸凹性和单调性;… 相似文献
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In this note, we study zeroes of Clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes: the real isolated zeroes and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes. 相似文献
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得到了复平面上忽略一点导数要求的扩充Hermite-Fejer插值多项式在|z|≤1上不一致收敛于f(z)∈A(|z|≤1)的结论,并得到了其平均收敛阶和内闭一致收敛性. 相似文献
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关于Bernstein型多项式导数的特征 总被引:4,自引:1,他引:4
利用高阶光滑模研究Bernstein型多项式的高阶导数问题,用函数的光滑性刻画Bernstein型多项式的高阶导数的特征,得到了一个等价定理。 相似文献